Subgroups — #26026217

Order 11392.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉⋊#401	C₂	1	2	yes	maximal
2	#19151539	C₂	1	6	yes	maximal
3	#19151504	C₂	1	3	yes	maximal
4	#19151496	C₂	1	3	yes	maximal
5	#376×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₈₉	C₂²	1	3	yes	—
8	C₂×#13083553	C₂²	1	6	yes	—
9	#15667919	C₂²	1	6	yes	—
10	#15667919	C₂²	1	6	yes	—
11	#15667919	C₂²	1	6	yes	—
12	C₂×C₄²×C₈₉	C₂²	1	3	yes	—
13	#95×C₈₉	C₂²	1	3	yes	—
14	#95×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₇₈	—	2	6	no	—
16	C₂²×Dic₈₉	C₂³	1	2	yes	—
17	C₂²×Dic₈₉	C₂³	1	6	yes	—
18	C₄⋊Dic₈₉	—	2	6	no	—
19	#13083553	—	4	6	no	—
20	C₂²×C₄×C₈₉	C₂³	1	3	yes	—
21	C₂²×C₄×C₈₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
23	C₄²×C₈₉	—	2	6	no	—
24	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₈₉	—	2	3	no	—
26	C₂×C₄×C₈₉	—	2	3	no	—
27	C₂×C₄×C₈₉	—	2	3	no	—
28	C₂×C₄×C₈₉	—	2	6	no	—
29	C₂×C₄×C₈₉	—	2	3	no	—
30	C₂×C₄×C₈₉	#41	1	6	yes	—
31	C₂×Dic₈₉	—	2	6	no	—
32	C₂×Dic₈₉	—	2	6	no	—
33	C₂×Dic₈₉	—	2	6	no	—
34	C₂×Dic₈₉	—	2	6	no	—
35	Dic₁₇₈	—	4	4	no	—
36	C₂²×C₈₉	C₂×#41	1	3	yes	—
37	C₂²×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
38	C₂²×C₈₉	2₋¹⁺⁴	1	3	yes	—
39	C₄×C₈₉	—	4	3	no	—
40	C₄×C₈₉	—	4	3	no	—
41	C₄×C₈₉	#126	1	4	yes	—
42	Dic₈₉	—	4	2	no	—
43	Dic₈₉	—	4	6	no	—
44	C₂×C₈₉	C₂×#126	1	1	yes	characteristic
45	C₂×C₈₉	#541	1	3	yes	—
46	C₂×C₈₉	#542	1	3	yes	—
47	#2645	—	89	1	no	maximal, Sylow
48	C₈₉	#2645	1	1	yes	characteristic, complemented, Sylow
49	#401	—	89	2	no	—
50	#400	—	89	6	no	—
51	#391	—	89	3	no	—
52	#389	—	89	3	no	—
53	#376	D₈₉	1	1	yes	characteristic
54	C₂²×Q₈	—	89	1	no	—
55	C₂×C₄⋊C₄	—	89	6	no	—
56	C₂×C₄⋊C₄	—	89	3	no	—
57	C₂×C₄²	C₂×D₈₉	1	3	yes	—
58	#95	—	89	6	no	—
59	#95	—	89	6	no	—
60	#95	—	89	6	no	—
61	#95	C₂×D₈₉	1	3	yes	—
62	#95	C₂×D₈₉	1	1	yes	characteristic
63	C₂×Q₈	—	178	6	no	—
64	C₂²×C₄	—	89	2	no	—
65	C₂²×C₄	—	89	6	no	—
66	C₂²×C₄	C₂²×D₈₉	1	3	yes	—
67	C₂²×C₄	C₂²×D₈₉	1	3	yes	—
68	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
69	C₄⋊C₄	—	356	6	no	—
70	C₄⋊C₄	—	178	6	no	—
71	C₄²	—	2	6	no	—
72	C₂³	C₂³×D₈₉	1	1	yes	characteristic
73	Q₈	—	356	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	178	6	no	—
80	C₂×C₄	—	178	6	no	—
81	C₂×C₄	—	178	6	no	—
82	C₂×C₄	—	178	6	no	—
83	C₂×C₄	#13083574	1	6	yes	—
84	C₂²	C₂×#13083574	1	3	yes	—
85	C₂²	#15668058	1	1	yes	characteristic
86	C₂²	#15668059	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	356	6	no	—
90	C₄	—	356	2	no	—
91	C₄	#15668006	1	4	yes	—
92	C₂	C₂×#15668006	1	1	yes	characteristic
93	C₂	#19152210	1	3	yes	—
94	C₂	#19152219	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₈₉
commutator, socle, prime radical, cosocle	C₂³×C₈₉	C₂⁴
Fitting	#376×C₈₉	C₂
hypercenter	#376	D₈₉
hypocenter	C₈₉	#2645
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ #376

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
48. C₈₉	#2645	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₉⋊#401	2
#19151539	2
#19151504	2
#19151496	2
#376×C₈₉	2
#2645	89